1. Field of the Invention
The present invention relates to a generation method, a creation method, an exposure method, a device fabrication method, a storage medium, and a generation apparatus.
2. Description of the Related Art
In the optical lithography technology, the pattern of an original (a mask or a reticle) used to form a pattern having a dimension less than a specific wavelength on a substrate such as a wafer does not always become similar to the pattern formed on the substrate, due to factors associated with correction of the optical proximity effect. Techniques of optimizing the pattern of an original have conventionally been proposed. Japanese Patent Laid-Open Nos. 2004-221594 and 2008-040470 propose techniques of determining an appropriate position for an auxiliary pattern (a pattern which itself is not resolved) in inserting the auxiliary pattern into a main pattern.
In the technique disclosed in Japanese Patent Laid-Open No. 2004-221594, a TCC (Transmission Cross Coefficient) must be calculated to calculate an interference map used to determine a position at which an auxiliary pattern is to be inserted. Hence, this technique requires an enormous amount of calculation and therefore requires a longer calculation time and a high-capacity computer memory.
The technique disclosed in Japanese Patent Laid-Open No. 2008-040470 can obtain a position at which an auxiliary pattern is to be inserted, with an amount of calculation which is smaller than that required in the technique disclosed in Japanese Patent Laid-Open No. 2004-221594. However, because there is little need to insert an auxiliary pattern in determining the pattern of a halftone mask serving as an original, Japanese Patent Laid-Open No. 2008-040470 discloses no embodiment in which a position at which an auxiliary pattern is to be inserted on the halftone mask is obtained. This is because a halftone mask is used to form a pattern having a large pitch more often than a binary mask, and the use of a halftone mask makes it possible to easily obtain a depth of focus larger than the use of a binary mask. Also, when an auxiliary pattern is inserted on a halftone mask using the same criterion as in a binary mask, the contrast may decrease.
Under such circumstances, a method of effectively increasing the depth of focus of a halftone mask with a smaller amount of calculation has not yet been proposed in the techniques of optimizing the pattern of an original. However, to keep pace with the growing demand for pattern miniaturization, a technique of forming a pattern having a smaller pitch using a halftone mask is in demand.